@inbook{fe8f56a063c5473a9da4795f3505a041,

title = "Two recent p-adic approaches towards the (effective) Mordell conjecture",

abstract = " We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usually called the method of Chabauty--Kim or non-abelian Chabauty in the literature, has the advantage that in some cases it has been turned into an effective method to determine the set of rational points on a curve, and we illustrate this by presenting three new examples of modular curves where this set can be determined. ",

keywords = "math.NT, math.AG",

author = "Balakrishnan, {Jennifer S.} and Best, {Alex J.} and Francesca Bianchi and Brian Lawrence and M{\"u}ller, {J. Steffen} and Nicholas Triantafillou and Jan Vonk",

year = "2021",

doi = "10.1007/978-3-030-65203-6_2",

language = "English",

isbn = "978-3-030-65202-9",

series = "Progress in Mathematics",

publisher = "Springer",

pages = "31--74",

editor = "A Chambert-Loir and J-H. Lu and M. Ruzhansky and Y. Tschinkel",

booktitle = "Regulators IV",

}